Session SC41 - Computational Investigations of the Foundations of Statistical Mechanics.
INVITED session, Wednesday afternoon, March 24
Liberty Room, Omni Hotel
The "effective action" provides a complete description of the statistical dynamics of both classical and quantum systems, more generally applicable than stochastic Langevin equations or master equations of the Fokker-Planck type. It generalizes to far-from-equilibrium systems the Onsager-Machlup action and thus provides a variational "least dissipation" characterization of mean histories. It encodes as well all multi-time statistics of arbitrary order. We describe some of our efforts to develop the "effective action" as a practical computational tool in predicting multi-time statistics of many-degree-of-freedom systems. The starting point is a theorem characterizing the effective action as a stationary point of the microscopic action functional under constrained variations, due in quantum field theory to Jackiw and Kerman. This allows a formulation of Rayleigh-Ritz variational methods to calculate the effective action, by making intuitive Ansätze for the system statistics. The method has close connections with traditional moment closure methods, but extends their capability to predicting multi-time correlations and provides a statistical foundation (H-theorems, fluctuation-dissipation relations, etc.) We shall describe some selected applications, which may include fluid turbulence governed by Navier-Stokes dynamics, aging behavior of glassy systems, or multi-time statistics of phase-ordering dynamics.